Game Theory and the Situation in North Korea: Time To Rethink Our Models?

A recent article by Oliver Roeder from FiveThirtyEight starts off with a game:

Imagine that a crisp $100 bill lies on a table between us. We both want it, of course, but there’s no chance of splitting it — our wallets are empty. So we vie for it according to a few simple rules. We’ll each write down a secret number — between 0 and 100 — and stick that number in an envelope. When we’re both done, we’ll open the envelopes. Whichever of us wrote down the higher number pockets the $100. But here’s the catch: There’s a percentage chance that we’ll each have to burn $10,000 of our own money, and that chance is equal to the lower of the two numbers.

So, for example, if you wrote down 10 and I wrote down 20, I’d win the $100 … but then we’d both run a 10 percent risk of losing $10,000. This is a competition in which, no matter what, we both end up paying a price — the risk of disaster.

Now imagine that you’re playing the same game, but for much more than $100. You’re a head of state facing off against another, and the risk you run is a small chance of nuclear war. The $100 prize becomes the concession of some international demand — a piece of disputed territory, say — while the $10,000 potential cost becomes untold death and destruction, nuclear winter and the very fate of our species and planet.

How would you play the game then?

This kind of game has been played before. In fact, this particular game is one example used in game theory, an approach to understanding conflicts and cooperation. And the application of game theory to war situations (and especially to nuclear war) comes from Thomas Schelling, a Nobel laureate and economist who worked for the Truman administration - Truman, as you may recall, was the President who made the decision to drop two nuclear weapons on Japan, the only President to drop nuclear bombs on another country as an act of war.

Schelling even wrote a book on his economic analysis of incentives, behaviors, and consequences - for which you can find full text here.

Nuclear weapons change the nature of the game. Before, the size and skill of the nation's army had a strong impact on whether it would win a battle, and eventually the war. There isn't a perfect relationship, of course, and there is a lot to say for strategy and the selection of allies. But if two countries have nuclear weapons, they can do immense damage to the other, even if they are in terms of manpower smaller and weaker.

So playing the game of war with nuclear weapons becomes less about the accuracy of the archers, and more about convincing the other country's leader that you're a risk taker who will not hesitate to launch some nukes. What happens when both leaders do this?

Game theory isn’t a perfect vessel. There are more than two players in today’s nuclear standoff, for example. China, South Korea, Japan and Russia all have their own $100 bills to gain. And, of course, the people involved in any game aren’t necessarily always rational. We often hear that Kim Jong Un, for example, is a madman — “We can’t let a madman with nuclear weapons let on the loose like that,” Trump once told the president of the Philippines.

But theorists do not begin their work from the premise that people or states are hyper-calculating rationality machines. Rather, they start from the reasonable notion that people respond to incentives. And madman or not, Kim will certainly respond to the disincentive of his country being blown to kingdom come.

Let's hope for all our sakes that both Kim and Trump will respond to those disincentives.